The Francesca Beale Theater at Lincoln Center is hosting a run of “Keane,” director Lodge Kerrigan’s 2005 film about a missing child, upon the occasion of its transferral to a high-resolution 4K format from a 35mm camera negative. Those of us who missed the picture during its initial release will have to take it on faith that the “new” version is of a better or, at least different, visual quality. 

Given the uncompromising tactility of the current version — “Keane” has to be among the grubbiest films extant — one can’t help but wonder how Mr. Kerrigan, along with editor Kristina Boden, altered or amplified the film. The original qualified as its own kind of transformation, being a remake of “In God’s Hands” starring Maggie Gyllenhaal and Peter Sarsgaard. That picture, also helmed by Mr. Kerrigan, never saw the light of day due to the film stock being irreparably damaged. This is a movie that’s been around the block.

The majority of “Keane” is centered around the labyrinthian accumulation of hallways, byways, and dead-ends that is Manhattan’s Port Authority. We first see William Keane (Damian Lewis, before his roles in “Homeland” and “Billions”) head to a ticket counter and ask the attendants if they remember seeing his daughter. Sophia has gone missing, you see, her father having lost sight of her in the bus terminal some months ago. The perplexity of those behind the counter is as patent as Keane’s desperation. The film begins on a frantic note, and rarely lets up.

Who is Keane? Mr. Kerrigan, who wrote the screenplay, doesn’t provide much in the way of a back story. Our protagonist is troubled, that’s for sure, and lives in a fleabag hotel near the Lincoln Tunnel. Disability checks seem to be his lone source of income, and much of those funds go to pay for alcohol, cocaine, and sex-on-the-fly. 

As he prowls the corridors of Port Authority, Keane engages in a running commentary about his daughter, his ex-wife, appropriate public behavior, and whether the stranger he just pummeled on Eighth Avenue was, in fact, his child’s abductor.

A question that’s never quite settled is whether our protagonist’s capacity to think rationally has been affected by the kidnapping or if he has, instead, long suffered from some kind of psychological disability. As we watch Keane rifle through newspaper clippings relating to another case involving an abducted child, we begin to wonder if Sophia existed at all. At other moments, Keane gives way to frantic soliloquies intimating that he is not a bereaved parent, but, rather, the victim of delusion.

This ambiguity of character — let’s not call it “vagueness” — is a sticking point to our being fully engaged with Keane’s plight and, for that matter, the film overall. Willful obscurantism is, in the long term, no friend to artistic immersion. The claustrophobic nature of Mr. Kerrigan’s direction — the camera, hand-held and rarely still, is invariably only a few feet away from Mr. Lewis — doesn’t help. As a cinematic experience, “Keane” is as trying as it intends to be. 

Thank goodness, then, for the introduction of Lynn and Kira Bedik (respectively, Amy Ryan and Abigail Breslin), a mother and daughter who live down the hallway from Keane. A tentative relationship is struck between the two adults, and Kira? She’s close to the age of Keane’s lost daughter — dangerously so, one might add. The kindness generated between Lynn and Keane — dinner and a fumbled attempt at dancing — brings a welcome tenderness to the film. 

Anxiety, as well. When Lynn abruptly skips town to track down her errant husband, Kira is left in Keane’s care. He proves a cautiously renewed man, but for how long? Mr. Kerrigan coasts on the audience’s good will, wishing the best for characters whose lack of fortune seems simultaneously navigable and overwhelming. That the denouement carries with it the barest wisp of hope does much to redeem Mr. Kerrigan’s sometimes shaky hold on his material. It is within these grace notes, and, especially, in the performance by Ms. Breslin, that “Keane” thrives.